QUESTION 1
A conical cup is 4 cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2 cm/sec. How fast (in cm/sec) is the water level dropping
when the height of the water is 3 cm?(Round your answer two (2) decimal places)
Answers
The water level will be dropping at the rate of [tex]0.64 cm/sec[/tex] when the height of the water reaches [tex]3cm[/tex]
We are give a cone with dimensions as seen in the diagram in the attached image.
The volume changes at the rate
[tex]\frac{dV}{dt}=-2cm^2/sec[/tex]
the negative sign is used because the volume of water is reducing.
what we need to know is the rate the height is changing when [tex]h=3cm[/tex]. That is, we need to evaluate
[tex]\frac{dh}{dt}|_{h=3cm}[/tex]
The relationship between the volume and the height is given by
[tex]V=\frac{1}{3}\pi r^2h[/tex]
but both [tex]h[/tex] and [tex]r[/tex] are changing when [tex]V[/tex] changes. So we need to eliminate [tex]r[/tex] somehow. From the diagram, we can use the similar triangle property to accomplish this
[tex]\frac{r}{2}=\frac{h}{6}\\\\\implies r=\frac{h}{3}[/tex]
substitute into the volume formula to eliminate [tex]r[/tex]
[tex]V=\frac{\pi h^3}{27}[/tex]
differentiate both sides with respect to time, [tex]t[/tex], since both the volume and height are functions of time. They will both be differentiated implicitly
[tex]\frac{dV}{dt}=\frac{\pi h^2}{9}\frac{dh}{dt}[/tex]
to find [tex]\frac{dh}{dt}|_{h=3cm}[/tex], substitute the values for [tex]\frac{dV}{dt}[/tex] and [tex]h[/tex]
[tex]-2=\frac{\pi 3^2}{9}\frac{dh}{dt}\\\\\frac{dh}{dt}=-\frac{2}{\pi}\\\\\approx -0.64 cm/sec[/tex]
So the rate at which the height is reducing when it reaches [tex]3cm[/tex] is [tex]0.64cm/sec[/tex]
Learn more about related rate of change here: https://brainly.com/question/15576763
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Answer:
the answer should be 2.5
Step-by-step explanation:
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Answers
The next step in constructing an angle (MNO ) congruent to the given angle (ABC ) is, using N as the center and the same radius as before, draw an arc that intersects |NO|. label the arc PQ where Q intersects |NO|.
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Answers
Answer:
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Step-by-step explanation:
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Luke portrays this time in Jesus’ ministry as very successful, but he starts giving hints of things to come. For instance, after the healing of the boy, Jesus seems to randomly say that he is going to be betrayed. Why would Jesus have picked that time to say such a thing? I think Jesus picked this time to warn the disciples about what was going to happen.
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Cost of 6 tickets = $ 96
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______
Hope it helps ⚜
Step-by-step explanation:
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Answer:
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Similar figures have equal ratios of corresponding sides:
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Answers
Answer:
7
Step-by-step explanation:
7
In 2020 researchers took random samples to compare the proportion of adult females to the proportion of adult males who use 2 or more credit/debit cards. The adults were aged 21 and older and they lived in all areas of the U.S. Based on the data collected, the researchers computed a 96 percent confidence interval for the true difference between the proportions of adult females minus the proportion of adult males who use 2 or more credit/debit cards. The confidence interval is: (0.013, 0.049). Assume all checks have been verified.
Question:
Choose the best answer below concerning the confidence interval for the difference between the true proportions of adult females minus the true proportion of adult males who use 2 or more credit/debit cards.
Answers
Using the z-distribution, it is found that the correct option is:
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A confidence interval is given by:
[tex]p \pm zs[/tex]
In which:
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[tex]s_1 = \sqrt{\frac{p_1(1 - p_1)}{n_1}}, s_2 = \sqrt{\frac{p_2(1 - p_2)}{n_2}}[/tex]
When two proportions are subtracted, the estimate is the subtraction of proportions, while the standard error of the subtraction is the square root of the sum of each standard error squared, hence:
[tex]p = p_1 - p_2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
Thus, the interval is:
[tex]p_1 - p_2 \pm z\sqrt{\frac{p_1(1 - p_1)}{n_1} + \frac{p_2(1 - p_2)}{n_2}}[/tex]
A similar problem is given at https://brainly.com/question/12517818
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Answer:
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Cross multiply and solve for x.
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Answers
Answer:
See image.
Step-by-step explanation:
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Answers
Answer:
G
Step-by-step explanation:
Therefore, the option [tex]G(-1,1)[/tex] is correct.
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An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here given inequality equation
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When the points [tex](-1,1)[/tex] so it would be
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Hence, the option [tex]G(-1,1)[/tex] is correct.
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HELP
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Answer:
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Step-by-step explanation:
6^2 = 36
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Answer:
Step-by-step explanation:
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Answer:
1: 2.8
Step-by-step explanation:
15:42
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Answer:
y = x/3 - 6
Step-by-step explanation:
yeah-ya......... right?
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Answer:
Any equation with a slope of 3 will work. You can use any y-intercept. This equation will work: y = 3x+1
Step-by-step-explanation:
3x says that the slope is 3, and on a coordinate plane, 2 is 3 places above 5, and since the slope is 3, it will go 3 spots up, and run into (0,2)
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Answer:
Sample Response: Since the statement is true, there are an infinite number of solutions to the system. This statement also indicates that the lines are equivalent.
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Answer:
7/8 , 5/6
Explanation:
7/8 , 5/6 are the only fractions that are not equivalent fractions as when they are simplified they don't share the same fraction. Hope this helps.
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Is ABC scalene, isosceles, or equilateral?
Answers
Answer:
isoselses!
Step-by-step explanation:
i hope that helps
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Answer:
2-3j
Step-by-step explanation:
Distribute 1/3 to the rest of the equation and you'll get 2-3j
I hope this helps!
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State the postulate or theorem you would use to prove each pair of triangles congruent.
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b) SAS
c) ASA
d) AAS
e) HL
f) Not possible
Answers
Answer:
f) Not possible
Step-by-step explanation:
The triangles can be shown to be similar by SAS, but the corresponding sides are not marked as congruent. With the given information, it is not possible to show the triangles are congruent.
What is the sum of the coefficients in the expression below?
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Answers
Answer:
485y to the power 2 + 5x to the power 2 - 6xy to the power 3 + 7
Step-by-step explanation:
I hope this helps. Also, there's this free app called Quick Math. If you need the steps, you should check there first, and maybe you should try that for other math problems as well.
Good luck and have a great rest of your day.
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students were surveyed ?
Answers
Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:
375 x 2 = 750
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Write a congruence statement and give a reason why the triangles are congruent. Select the correct choice below and, if necessary, write the vertices of the second triangle in the correct order.
Answers
Answer:
option B is correct answer. ∆SVZ~=∆YVX, SSS
Step-by-step explanation:
reasons,
VY=VS, S
YX=SZ, S
VX=VZ, S
therefore, ∆SVZ~=∆YVX.
hope this helps you.
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